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67. a. Use a CAS to evaluate 7/2 sin" x dx sin" x + cos" x where n is an arbitrary positive integer. Does your CAS find the result? b. In succession, find the integral when n = 1, 2, 3, 5, and 7. Comment on the complexity of the results. c. Now substitute x = (7/2) – u and add the new and old integrals. What is the value of /2 sin" x dx? sin" x + cos" x This exercise illustrates how a little mathematical ingenuity solves a problem not immediately amenable to solution by a CAS.

67. a. Use a CAS to evaluate 7/2 sin" x dx sin" x + cos" x where n is an arbitrary positive integer. Does your CAS find the result? b. In succession, find the integral when n = 1, 2, 3, 5, and 7. Comment on the complexity of the results. c. Now substitute x = (7/2) – u and add the new and old integrals. What is the value of /2 sin" x dx? sin" x + cos" x This exercise illustrates how a little mathematical ingenuity solves a problem not immediately amenable to solution by a CAS.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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67. a. Use a CAS to evaluate 7/2 sin" x dx sin" x + cos" x where n is an arbitrary positive integer. Does your CAS find the result? b. In succession, find the integral when n = 1, 2, 3, 5, and 7. Comment on the complexity of the results. c. Now substitute x = (7/2) – u and add the new and old integrals. What is the value of /2 sin" x dx? sin" x + cos" x This exercise illustrates how a little mathematical ingenuity solves a problem not immediately amenable to solution by a CAS.
Transcribed Image Text:67. a. Use a CAS to evaluate 7/2 sin" x dx sin" x + cos" x where n is an arbitrary positive integer. Does your CAS find the result? b. In succession, find the integral when n = 1, 2, 3, 5, and 7. Comment on the complexity of the results. c. Now substitute x = (7/2) – u and add the new and old integrals. What is the value of /2 sin" x dx? sin" x + cos" x This exercise illustrates how a little mathematical ingenuity solves a problem not immediately amenable to solution by a CAS.
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